H varies as V and inversely as the square of r.Find the percentage change in H if V is increased by 20%and at the same time r is increased by 50%

Answer 1

To find the percentage change in H, we need to determine how the change in V and r affects H.

First, let's establish the equation relating H, V, and r:
H = k * (V / r^2)
where k is the constant of variation.

Now, let's consider the given changes:
1. V is increased by 20%: V_new = V + 0.2V = 1.2V
2. r is increased by 50%: r_new = r + 0.5r = 1.5r

Substitute the new values into the equation:
H_new = k * (V_new / r_new^2)
= k * (1.2V / (1.5r)^2)
= k * (1.2V / 2.25r^2)
= (1.2/2.25) * k * (V / r^2)
= 0.533333... * H

The new value of H is 0.533333... times the original value of H. Therefore, there is a 46.67% decrease in H if V is increased by 20% and r is increased by 50%.